In this paper, we first introduce the notion of a completion. Completions are inductive properties which may be expressed in a declarative way and which may be combined. In the sequel of the paper, we show that completions may be used for describing structures or transformations which appear in combinatorial topology. We present two completions, 〈Cup〉 and 〈Cap〉, in order to define, in an axiomatic way, a remarkable collection of acyclic complexes. We give few basic properties of this collection. Then, we present a theorem which shows the equivalence between this collection and the collection made of all simply contractible simplicial complexes. © 2011 Springer-Verlag.
CITATION STYLE
Bertrand, G. (2011). Completions and simplicial complexes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6607 LNCS, pp. 129–140). https://doi.org/10.1007/978-3-642-19867-0_11
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